Chapter 9.1, Problem 10PSB

a

To determine

To calculate: The Value of xin the given expression i.e. $3x^2+5x-7=x^2+8x+28$

Answer to Problem 10PSB

Values of x are $\frac{-7}{2}$ and $5$ .

Explanation of Solution

Given information:Equation: $3x^2+5x-7=x^2+8x+28$

Calculation: $3x^2+5x-7=x^2+8x+28$

  $\begin{array}{l}\Rightarrow 3x^2-x^2+5x-8x-7-28=0\\ \Rightarrow 2x^2-3x-35=0\\ \Rightarrow 2x^2-10x+7x-35=0\\ \Rightarrow 2x(x-5)+7(x-5)=0\\ \Rightarrow (2x+7)(x-5)=0\end{array}$

  $\Rightarrow 2x+7=0$ and $x-5=0$

  $\Rightarrow 2x=-7$ and $x=5$

  $\Rightarrow x=\frac{-7}{2}$ and $x=5$

b

To determine

To calculate:The Value of xin the given expression i.e. $8x^2-7x+9=2x^2+6x+7$

Answer to Problem 10PSB

Values of x are $\frac{-1}{6}$ and $2$ .

Explanation of Solution

Given information:Equation: $8x^2-7x+9=2x^2+6x+7$

Calculation: $8x^2-7x+9=2x^2+6x+7$

  $\begin{array}{l}\Rightarrow 8x^2-2x^2-7x-6x+9-7=0\\ \Rightarrow 6x^2-13x+2=0\\ \Rightarrow 6x^2-12x-x+2=0\\ \Rightarrow 6x(x-2)+1(x-2)=0\\ \Rightarrow (6x+1)(x-2)=0\end{array}$

  $\Rightarrow 6x+1=0$ and $x-2=0$

  $\Rightarrow 6x=-1$ and $x=2$

  $\Rightarrow x=\frac{-1}{6}$ and $x=2$

c

To determine

To calculate:The Value of xin the given expression i.e. $12x^2-15=-11x$

Answer to Problem 10PSB

Values of x are $\frac{3}{4}$ and $\frac{-5}{3}$ .

Explanation of Solution

Given information:Equation: $12x^2-15=-11x$

Calculation: $12x^2-15=-11x$

  $\begin{array}{l}\Rightarrow 12x^2+11x-15=0\\ \Rightarrow 12x^2+20x-9x-15=0\\ \Rightarrow 4x(3x+5)-3(3x+5)=0\\ \Rightarrow (4x-3)(3x+5)=0\end{array}$

  $\Rightarrow 4x-3=0$ and $3x+5=0$

  $\Rightarrow 4x=3$ and $3x=-5$

  $\Rightarrow x=\frac{3}{4}$ and $x=\frac{-5}{3}$